A137710 Triangle read by rows: T(n,k) = T(n-1, k-1) - T(n-k, k-1) for k > 1 with T(n,1) = 2^(n-1).

1, 2, 1, 4, 1, 1, 8, 2, 1, 1, 16, 4, 1, 1, 1, 32, 8, 3, 1, 1, 1, 64, 16, 6, 2, 1, 1, 1, 128, 32, 12, 5, 2, 1, 1, 1, 256, 64, 24, 11, 4, 2, 1, 1, 1, 512, 128, 48, 21, 10, 4, 2, 1, 1, 1, 1024, 256, 96, 42, 20, 9, 4, 2, 1, 1, 1, 2048, 512, 192, 84, 40, 19, 9, 4, 2, 1, 1, 1

Offset

1,2

Comments

The triangle is generated by two rules: T(n,k) = T(n-1, k-1) - T(n-k, k-1); and left border = 1, 2, 4, 8, 16, ...

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Example

First few rows of the triangle:
    1;
    2,   1;
    4,   1,  1;
    8,   2,  1,  1;
   16,   4,  1,  1,  1;
   32,   8,  3,  1,  1, 1;
   64,  16,  6,  2,  1, 1, 1;
  128,  32, 12,  5,  2, 1, 1, 1;
  256,  64, 24, 11,  4, 2, 1, 1, 1;
  512, 128, 48, 21, 10, 4, 2, 1, 1, 1;
  ...

Prog

(PARI)
MtxA137710(n, m=n)=my(M=matrix(n, m)); for(i=1, n, M[i, 1]=2^(i-1); for(j=2, i, M[i, j] = M[i-1, j-1] - if(i>=2*j-1, M[i-j, j-1]) )); M
{ my(M=MtxA137710(12)); for(i=1, #M, print(M[i, 1..i])) } \\ Andrew Howroyd, Sep 22 2025

Crossrefs

Row sums are A137711.

Column 1 is A000079(n-1).

Cf. A137712, A180339.

Sequence in context: A088443 A117352 A393918 * A068009 A140168 A059119

Adjacent sequences: A137707 A137708 A137709 * A137711 A137712 A137713

Keyword

nonn,tabl

Author

Gary W. Adamson, Feb 08 2008

Extensions

Corrected by Andrew Howroyd, Sep 22 2025

Status

approved